Development of Multi-Layer 1D - PowerPoint Presentation

Slide1

Development of Multi-Layer 1D

divertor code and analysis of detached divertor plasmas

a

Satoshi Togo, bMakoto Nakamura, cKatsuhiro Shimizu,dTomonori Takizuka, bKazuo Hoshino, aYuichi Ogawa

aGraduate School of Frontier Science, University of Tokyo

bJapan Atomic Energy Agency, Aomori

cJapan Atomic Energy Agency, Ibaraki

dGraduate School of Engineering, Osaka University

第

16

回 若手科学者によるプラズマ研究会

2013/03/04-06 @Naka, JAEA

Back ground

Divertor

heat load

2CorePlasmaPout

Pout ～

90MW(ITER)

The wetted area is a few square meters so some sort of power handling is necessary.

The divertor heat load have to be 5~6MW/m2 at most from the material point of view.

P

out

～

500MW

(Slim-CS)

Reduction of t

he

divertor

heat load is one of the crucial issues for commercializing the fusion reactors.

Divertor

detachment

3

N. Ohno and S. Takamura, J. Plasma Fusion Res. 84, No.11, 740-749 (2008).S. Takamura, J. Plasma Fusion Res. 72, No.9, 866-873 (1996).

Divertor detachment is thought to be a promising way.

Back ground

Two-dimensional SOL-

divertor code

Numerical grid for JT-60U in the SONIC simulation

4The electron temperature and the parallel ion flux as a function of the mid-plane densityK. Hoshino et al., J. Plasma Fusion Res. Ser. 9, 592-597 (2010).

2D codes are used in order to estimate rigorously the performance of the divertor.

In simulating detached divertor regime, there are some

quantitative disagreements with the experimental results.Back ground

Purpose of our research

5

Core

Plasma

Detached

Tube

Attached

Tube

X-point

Magnetic Field

0

L

x

Schematic picture of ML 1D code

The characteristics of partially detached

divertor

plasmas in the perpendicular direction are reproduced with only two flux tubes.

http://www.lhd.nifs.ac.jp/

We have been developing Multi-Layer (ML) 1D

divertor

code so as to generate an understanding of the important processes for the quantitative reproduce of (partially) detached

divertor

plasmas.

ML 1D code

Basic equations

6

Mass conservation:

Momentum conservation:Energy conservation

:

Core

Plasma

Detached

Tube

Attached

Tube

X-point

Magnetic Field

0

L

x

Radial transport is included in the source terms.

Density, velocity and temperature of ion and electron

are assumed to be equal, respectively.

Source terms/Atomic processes

7

Particle source:

Momentum source:Energy source:

ML 1D code

S.

Takamura, J. Plasma Fusion Res. 72, No.9, 866-873 (1996).

Boundary condition

8

Stagnation point

(x = 0)

Divertor

plate

(x = L)

x=0

x=L

is the sheath heat transmission factor.

Core

Plasma

Detached

Tube

Attached

Tube

X-point

Magnetic Field

0

L

x

ML 1D code

Neutral model

9

Particle conservation

：S. Nakazawa et al., Plasma Phys. Control. Fusion 42, 401-413 (2000).

Convection with Franck-Condon Energy

Diffusion by charge exchange reaction

Boundary condition

：

Radial transport

ML 1D code

Neutralization rate

Calculation condition

10

Simulation has been done for ASDEX-Upgrade like plasma.

A. Kallenbach et al., Nucl. Fusion 48 085008 (2008).・Area of separatrix：40m2

・Width of the SOL：2cm

http://www.ipp.mpg.de/ippcms/eng/for/projekte/asdex/

・Minor radius a：0.6m

・Major radius R：

1.7m

・

Surface safety factor q

：

3.3

・

Connection length

πqR

：

17.6m

・

Divertor

leg

：

4.4m

・

Heat flux from the core plasma

：

4MW

・

Neutralization rate of the plate

η

：

99%

・

Impurity

：

Carbon, 1%, non-coronal equilibrium

ML 1D code

Attached plasma solution

11

Diffusion by the charge exchange is assumed to be dominant.

Particle flux from the core plasma is 1.0×1021 s-1.

[/m

3

]

[

eV

]

[/m

3

]

X

-point

Recent result

12

ION

NEUTRAL

Core

5×10

20

/s

Ionization

499×10

20

/s

Recycled

499×10

20

/s

Not recycled

5×10

20

/s

Neutralization

504×10

20

/s

At such temperature, volume recombination can’t dominate ionization so that detachment doesn’t occur.

Heat loss is too small to dissipate all of the heat flux from the core so that the temperature near the plate is relatively high.

[W]

Heat flux

Core

Imp.

CX

Ioniz

.

Recomb

.

[/s]

Particle

flux

Ioniz

.

Core

Recomb

.

Recent result

Attached plasma solution

13

The gradient of the neutral density profile near the plate is negative implying neutral flows toward the plate there.

[/m

3]

[eV][/m

3]

X-point

Recent result

Detached plasma solution

If radial neutral loss is large enough, τ

n

~10

-4

s, particle balance is accomplished and steady state solutions appear.

14

[W]

Heat flux

CoreImp.CX

Ioniz.

Recomb.Recomb.

Particle flux

Ioniz.

Core

[/s]

Recent result

Heat loss is large enough to dissipate all of the heat flux from the core so that the temperature near the plate is relatively low.

The temperature is low enough for volume recombination to dominate ionization so that detachment occurs.

ION

NEUTRAL

Core

2.5×10

22

/s

Ionization

6.2×10

22

/s

Radial loss

2.5×10

22

/s

Recombination

8.7×10

22

/s

Detached plasma solution

15

Conclusion

・ML 1D

divertor code has been developed. During the last year, numerical neutral model was introduced and numerical scheme was improved. The detached regime has been successfully reproduced.・Heat and particle balance in both attached and detached regime have been investigated indicating that the difference in the particle balance between attached and detached regime might be related to the formation of partially detached divertor plasma.・To distinguish the mechanism of neutral transport by means of their generation is our future work.